A top conservative group is pressing Rep. Mike Pence, R-Indiana, to run for Senate.

Washington (CNN) - In the wake of Republican Scott Brown's surprising win in this week's Senate special election in Massachusetts, the anti-tax Club for Growth is publicly urging Indiana Rep. Mike Pence, R-Indiana, to challenge Sen. Evan Bayh this fall.

Pence is a hero to small-government conservatives who has beefed up his political operation in recent months along with making travels to states like Iowa and South Carolina, sparking talk that he is eyeing a White House run in 2012. Pence has also been mentioned as a potential successor to Indiana Gov. Mitch Daniels after Daniels' second term expires in 2013.

But the Club for Growth wants Pence to jump in the Senate race instead. Chris Chocola, the Club's president, said in a statement Thursday that Brown's win in Massachusetts "confirms that Indiana is a winnable race for a principled advocate of economic freedom and limited government."

"Mike Pence can beat Evan Bayh in November, and I join pro-growth conservatives in Indiana and around the country in hoping that he does," Chocola said.

On Wednesday, Pence confidante Tony Perkins - the president of the conservative Family Research Council - suggested to CNN that Pence isn't likely to run against Bayh. "I think he is positioned to move, but I just don't know if the Senate is where he will be," Perkins said.

Pence, currently the House Republican Conference Chairman, is at least entertaining the idea. He is planning to meet with Sen. John Cornyn, the chairman of the National Republican Senatorial Committee, on Thursday afternoon. If he does decide to run, Pence would likely need some financial help from both the Club and the NRSC: Bayh has nearly $13 million in his campaign war chest, while Pence had just $463,000, according to his most recent financial report.

Mike Connolly, a spokesman for the Club, hinted that the group would be there financially if Pence takes the plunge this year.

"There is no question the Club and our members hold Mike Pence in very high regard," Connolly said. "People can draw their own conclusions about what that might mean."